The implications of 3D for solar MHD modelling

The effects of three-dimensionality on the modelling of solar magnetic fields are described. We focus on two processes that are believed to play an important role in coronal heating - the braiding of field lines by photospheric motions and the reconnection of colliding Bur tubes. First, it is shown that a proper treatment of boundary conditions at the photosphere in 3D entails qualitatively new physical processes that are not present in 2D. The numerical resolution of even simple boundary velocity patterns in 3D Leads to obstacles which have no counterpart in the 2D case. We conclude that adaptive mesh refinement is necessary for capturing the essential 3D physics of a braiding motion at the photosphere. Next, the effects of 3D on magnetic reconnection are discussed. Reconnection in 3D can lead to an evolution of interacting flux tubes, magnetic tunneling, that is not only impossible in lower dimensionality, but is strikingly counterintuitive. The implications of these results for the structure of the solar magnetic field and for coronal heating are described.